Hadamard and Fejér type inequalities for p-convex functions via Caputo fractional derivatives

[1] S. Abbaszadeh and A. Ebadian, Nonlinear integrals and Hadamard-type inequalities, Soft Comput. 22(9) (2018) 2843–2849.

[2] S. Abbaszadeh and M. E. Gordji, A Hadamard-type inequality for fuzzy integrals based on r-convex functions, Soft Comput. 20(8) (2016) 3117–3124.

[3] M.R. Delavar and S.S. Dragomir, Hermite-Hadamard’s mid-point type inequalities for generalized fractional integrals, Rev. Real Acad. Cien. Exactas, F´ısicas y Naturales. Serie A. Mate. 114(2) (2020) 1–14.

[4] M.R. Delavar, M. Rostamian and M. De La Sen, A mapping associated to h-convex version of the HermiteHadamard inequality with applications, J. Math. Inequal. 14(2) (2020) 329–335.

[5] M.R. Delavar, S.S. Dragomir and S.M. Aslani, Hermite-Hadamard-Fej´er inequality related to generalized convex functions via fractional integrals, J. Math. 2018 (2018).

[6] S.S. Dragomir and S. Fitzpatrick, The Hadamard’s inequality for s-convex functions in the second sense, Demonstratio Math. 32 (1999) 687–696.

[7] S. S. Dragomir, J. Pecaric and L. E. Persson, Some inequalities of Hadamard type, Soochow J. Math. 21 (1995) 335–341.

[8] G. Farid, A. Javed and S. Naqvi, Hadamard and Fejer-Hadamard inequalities and related results via Caputo fractional derivatives, Bull. Math. Anal. Appl. 9(3) (2017) 16–30.

[9] L. Fej´er, Uberdie fourierreihen, II, Math. Naturwise. Anz Ungar. Akad. Wiss (in Hungarian) 24 (1906) 369–390.

[10] J. Hadamard, Etude sur les proprietes des fonctions enti`eres et en particulier d’une fonction conside´ee par  Riemann, J. Math. Pures Appl., (1893) 171–215.

[11] Ch. Hermite, Sur deux limites d’une in´tegrale ´denie, Math. 3 (1883) 82.

[12] I. Iscan, Hermite-Hadamard type inequalities for p-convex functions, Int. J. Ana. Appl. 11(2) (2016) 137–145.

[13] F. Jarad, E. Ugurlu, T. Abdeljawad and D. Baleanu, On a new class of fractional operators, Adv. Difference Equ. 2017 (2017) 247.

[14] U. S. Kirmaci, M. K. Bakula, M. E. Ozdemir and J. Pecaric,  Hadamard-type inequalities for s-convex functions, Appl. Math. Comput. 193 (2007) 26–35.

[15] M. Kunt and I. Iscan, Hermite-Hadamard-Fejer type inequalities for p-convex functions, Arab. J. Math. Sci. 23 (2017) 215–230.

[16] N. Mehreen and M. Anwar, Integral inequalities for some convex functions via generalized fractional integrals, J. Inequal. Appl. 2018 (2018) 208.

[17] N. Mehreen and M. Anwar, Hermite-Hadamard type inequalities via exponentially p-convex functions and exponentially s-convex functions in second sense with applications, J. Inequal. Appl. 2019 (2019) 92.

[18] N. Mehreen and M. Anwar, Hermite-Hadamard type inequalities via exponentially (p, h)-convex functions, IEEE Access 8 (2020) 37589–37595.

[19] N. Mehreen and M. Anwar, On some Hermite-Hadamard type inequalities for tgs-convex functions via generalized fractional integrals, Adv. Diff. Equ. 2020 (2020) 6.

[20] N. Mehreen and M. Anwar, Hermite-Hadamard and Hermite-Hadamard-Fejer type inequalities for p-convex functions via conformable fractional integrals, J. Inequal. Appl. 2020 (2020) 107.

[21] N. Mehreen and M. Anwar, Hermite-Hadamard and Hermite-Hadamard-Fejer type inequalities for p-convex functions via new fractional conformable integral operators, J. Math. Compt. Sci. 19 (2019) 230–240.

[22] N. Mehreen and M. Anwar, Some inequalities via ψ-Riemann−Liouville fractional integrals, AIMS Math. 4(5) (2019) 1403–1415.
[23] M.Z. Sarikaya, E. Set, H. Yaldiz and N. Ba¸sak, Hermite-Hadamard’s inequlities for fractional integrals and related fractional inequalitis, Math. Comput. Model. 57 (2013) 2403–2407.

[24] E. Set, M. Z. Sarikaya, M. E. Ozdemir and H. Yaldirm, The Hermite–Hadamard’s inequality for some convex functions via fractional integrals and related results, J. Appl. Math. Stat. Inf. 10 (2014) 69–83.

[25] H. Vosoughian, S. Abbaszadeh and M. Oraki, Hadamard integral inequality for the class of harmonically (γ, η)- convex functions, Front. Funct. Equ. Anal. Inequal. (2019) 695–711.